Counting primes in the interval (n^2,(n+1)^2)

Mehdi Hassani

Counting primes in the interval (n^2,(n+1)^2)

Number Theory 2007-05-23 v1

Authors: Mehdi Hassani

Abstract

In this note, we show that there are many infinity positive integer values of $n$ in which, the following inequality holds $\left\lfloor{1/2}(\frac{(n+1)^2}{\log(n+1)}-\frac{n^2}{\log n})-\frac{\log^2 n}{\log\log n}\right\rfloor\leq\pi\big((n+1)^2\big)-\pi(n^2).$

Keywords

prime numbers multiplicative functions prime number theory

Cite

@article{arxiv.math/0607096,
  title  = {Counting primes in the interval (n^2,(n+1)^2)},
  author = {Mehdi Hassani},
  journal= {arXiv preprint arXiv:math/0607096},
  year   = {2007}
}

Comments

This is a three pages unsuccessful (but maybe useful) challenge, for proving the old-famous conjecture, which asserts for every positive integer n, the interval (n^2,(n+1)^2) contains at least a prime

Counting primes in the interval (n^2,(n+1)^2)

Abstract

Keywords

Cite

Comments

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